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The positions of stars on the sky are defined against a co-ordinate reference frame that is ultimately defined by the positions of very distant radio sources (quasars at high redshift) that are assumed to be "stationary" in terms of their celestial grid co-ordinates (see International Celestial Reference Frame) All stars can have their positions precisely ...
Spectroscopic parallax is the technique whereby you estimate the absolute magnitude (i.e. the brightness it would have if it were placed at 10 pc) by estimating what "type" of star it is using information fro a spectrum. It can be applied to any kind of star where (a) you have a reasonable chance of determining the type of star from its spectrum and (b) ...
$\theta$ is half the difference in direction of 2 measurements of the position of the star taken 6 months apart.
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